We illustrate the lower bound in (REF ) with an example involving common zeros of polynomials. We have the following result.
 Suppose \(Q_1,Q_2,\ldots ,Q_N\)  are \(N\)  homogenous polynomials in the variables \(x_1,\ldots ,x_m,\)  each with degree \(k.\)  If \(N \ge 1+q\cdot \left(\frac{q}{q-1}\right)^{k-1},\)  then there are indices \(1 \le i \ne j \le N\)  such that \(Q_i\)  and \(Q_j\)  have a common zero.

We remark here that the Chevalley-Warning theorem [1]} is used to describe conditions under which a set polynomials whose sum degree is smaller than the number of variables, all have more than one common root. In Proposition , we require that the number of polynomials is sufficiently large in order that at least two of the polynomials have a common root.
